Statistical Analysis for Education and Psychology Researchers

Figure 8.18: Output for One-way

repeated measures analysis of

variance

It is often informative to inspect any differences in means visually, a plot of the mean
reading accuracy scores for each measurement occasion is given by the following SAS
code:

*** To produce plot of means by treatment occasion ***;

proc sort; by time;

run;

proc means mean noprint data=b;

var score;

by time;

output out=means mean=score;

run;

proc plot data=means;

plot score*time;

run;

Interpretation of Computer Output

The usual plots to check for underlying assumptions should be performed before detailed
examination of the results. The SAS output is interpreted in exactly the same way as
described in the section on unrelated One-Way ANOVA, the only difference here is the
partitioning of a separate source of variance attributable to Subjects. Also note, The
Model sums of squares is equivalent to the total of the sums of squares for Subject and
Time.
As before, the first section of output in Figure 8.18 contains summary information on
the variables entered in the model. Here the variables subject and time are analysed, the
summary information shows there are five subjects, three occasions for time and a total
of fifteen observations.
The next section of output presents results of the analysis of variance, again an
investigator should first check that the degrees of freedom are correct. The sums of
squares for the model and error are presented first and then the model sums of squares is
partitioned into separate sources of variance, subject and time. A test of overall model fit
is given by the first F-value of 6.38 which is significant at the 1 per cent level (p=0.01).
This indicates that the sources of variance specified in the statistical model have a
significant effect on reading accuracy scores. F-statistics for the effects of individual
sources of variance are given in the following section of the output. We can conclude that
the mean reading accuracy score differs over the three measurement occasions, F=14.55;
df 2,8; p < 0.05 and there is no significant subject effect. Overall individual differences
among subjects are not significant at the 5 per cent level. The statistics in the SAS output
and the substantive conclusions are the same as in the worked example.
An investigator having identified a significant time effect may want to inspect this
further by examining any possible trends in the means. Clearly if this was a design
intention it would be preferable to have more than three repeated measures. One method

Statistical analysis for education and psychology researchers 332